Stat 104 Section 3 - Problem Solutions

Stat 104 Section 3 - Problem Solutions - Stat 104 Section...

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Stat 104 Section Notes 3 Problem Solutions 1a) I have 5 M&M’s left in the bag: 2 blue, 2 red, and 1 yellow. I plan on eating two more, and leaving the others in the bag. a) S = {(b 1 ,b 2 ), (b 1 ,r 1 ), (b 2 ,r 1 ), (b 1 ,r 2 ), (b 2 ,r 2 ), (b 1 ,y), (b 2 ,y), (r 1 , y), (r 2 ,y), (r 1 ,r 2 )} b) Describe the set of events for: A : A = {(b 1 ,r 1 ), (b 2 ,r 1 ), (b 1 ,r 2 ), (b 2 ,r 2 ), (b 1 ,y), (b 2 ,y), (r 1 , y), (r 2 ,y)} B : B = {(b 1 ,b 2 ), (b 1 ,r 1 ), (b 2 ,r 1 ), (b 1 ,r 2 ), (b 2 ,r 2 ), (b 1 ,y), (b 2 ,y)} c) What is the probability of: A: B: *Note: these simple probabilities could be calculated because we took some effort in defining our sample space carefully so that each element was equally like to occur. d) Are A & B disjoint? _ No __ How do you know? Because there are elements in both A and B (aka, the intersection is not empty). Disjoint means the 2two events have nothing in common, but these two events certainly do. e) Describe (in words and in terms of outcomes) the intersection of A & B ? and the union, A or B ? A and B = {(b 1 ,r 1 ), (b 2 ,r 1 ), (b 1 ,r 2 ), (b 2 ,r 2 ), (b 1 ,y), (b 2 ,y)} A and B = {(b 1 ,b 2 ), (b 1 ,r 1 ), (b 2 ,r 1 ), (b 1 ,r 2 ), (b 2 ,r 2 ), (b 1 ,y), (b 2 ,y), (r 1 , y), (r 2 ,y)} f) What is the probability of A & B ? A or B ? g) Are
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Stat 104 Section 3 - Problem Solutions - Stat 104 Section...

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